We study the problem of estimating the Receiver Operating Characteristic (ROC) curve under a standard binary classification setting. We formally introduce the notion of optimal ROC curve and derive its analytic form, which parallels the role of Bayes error in standard classification. It is argued that any ROC curve estimation methods should target the optimal ROC curve. Three popular ROC curve estimation methods are analyzed at the population level. Based on our theory, they are consistent when the surrogate loss functions satisfies certain conditions and the model space includes all measurable classifiers. Interestingly, some of these conditions are similar to those that are required to ensure classification consistency. When the model space is incorrectly specified, however, we show that only one method leads to consistent estimation of the ROC curve over the chosen model space. We present some numerical results to demonstrate the effects of model misspecification on the performance of various methods in terms of their ROC curve estimates.